Boxed Up to Go

The seemingly unwieldy shape of a fish is anything but a drag.

Until recently I would have bet I could tell a fast fish from a slow one by looking at the placement of its fins and the shape of its body. Boxfishes, with their fins at the corners of their “boxy” bodies, would not have made my list of speedsters on either count. But it turns out that boxfishes are fast, stable, and amazingly maneuverable swimmers—so much so as to inspire human designers.

Boxfishes get their name from the rectangular (or sometimes five-sided) shell of bony armor on the front two-thirds of their bodies. The eyes, mouth, and fins poke through holes in the covering, but otherwise the fish’s body surface is an uninterrupted mosaic of hexagonal tiles of bone.

The edges of the bony box act as keels, running nearly the entire length of the fish. In some boxfishes, such as the aptly named cowfishes, the keels extend forward, beyond the body, to form sharp horns. Like its relative the puffer fish, the boxfish propels itself by waving its dorsal fin (on top of its body )and its anal fin (on the bottom), and it steers primarily with its pectoral fins and tail fin. Both dorsal and anal fins are situated well to the rear of the fish.

I assumed the hydrodynamic properties of a boxfish were comparable to those of a square compact car or an SUV—a vehicle that’s good for carrying loads, with neither speed nor agility. But Ian K. Bartol, a biologist at Old Dominion University in Norfolk, Virginia, and a multidisciplinary team of investigators have proved, once again, the limits of intuition. First, they point out, far from being slowpokes, boxfishes can scoot over a reef at six body lengths per second—an impressive speed by any standard. Moreover, Bartol and company managed to visualize the flow of water around a boxfish by placing neutrally buoyant beads in the water and filming the beads as they swept past plastic models of the fish. They found, with their models, that the drag of the boxfish is surprisingly low, as expressed by a dimensionless quantity known as its drag coefficient. The drag coefficient of the boxfish is just 0.2, which is comparable to some streamlined airfoils, and falls well below 1.5, the drag coefficient of a flat-faced box.

At first glance, those hydrodynamic properties are puzzling. The dorsal and anal fins, which push the fish along, are way off the central axis of its body, yet the animal swims a straight path without rocking up and down. That would seem to require either perfect coordination of two fins of widely differing shape and size, or a trick that somehow imparts stability to the fish without slowing it down.

When the boxfish swims up (top), spiral vortices develop above its four “edges,” or keels. The vortices create a low-pressure zone, strongest at the rear of the fish, which tends to pull the tail end of the fish up (yellow arrows) and so help keep it level and stable. In a downward dive (bottom), the boxfish generates vortices below its four keels. The low pressures in the vortices help pull the tail end of the fish down (yellow arrows).

Tom Moore

Bartol and his colleagues found that the secret to the dynamic stability of the boxfish lies in the keels that form the edges of the box. The keels set up strong spiral vortices of water that flow along the keels, hugging close to the surface of the fish and intensifying at the rear end. When the fish tilts nose-up, the vortices develop above the keels; when it tilts down, the vortices form below the keels [see illustrations left].

The pressure of the water in these swirling vortices is lower than it is in the undisturbed fluid around the fish. Hence as the nose tilts up, a low-pressure vortex above the keels tends to pull the body upward, leveling it. Similarly, as the nose goes down, the vortices below the keels tend to counteract the upward tilt of the tail end. The pectoral fins, furthermore, are well placed to interrupt or adjust the vortices, and those fins can also act to stabilize the body or propel the fish into a speedy turn.

The beauty of the fish’s solution to the problem of propulsion and stabilization is that the functioning of the keels is entirely passive. In other words, it requires no active control from the fish. The vortices automatically stabilize a motion that might otherwise lead to very inefficient head bobbing. Not only is little energy required of the fish, but there are also no complex neural circuits needed for control; a clever set of immovable strakes, shaping the body from stem to stern, lets geometry, and fluid dynamics, do all the work “for free.”

Computer-generated model of a car with design elements inspired by the hydrodynamically efficient boxfish.

Tom Moore

Mercedes-Benz has already taken note of this nice combination of load carrying and low drag. In fact, the boxfish is the basis for the automobile company’s latest concept car. The result is a boxfish on wheels, with headlights, windows, and a very slippery drag coefficient of just 0.19—comparable to an airfoil. The vehicle even emulates the hexagonal tiles of the fish’s carapace to create strong, lightweight doors. The producers of the next James Bond movie might take a cue from the new design: this car would be an agile underwater performer, with built-in armor and lots of cargo space for spy gear.